Question: Simplify the following expression: $ z = \dfrac{4p + 5}{-8p} + 3 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-8p}{-8p}$ $ \dfrac{-3}{1} \times \dfrac{-8p}{-8p} = \dfrac{24p}{-8p} $ Therefore $ z = \dfrac{4p + 5}{-8p} - \dfrac{24p}{-8p} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{4p + 5 - 24p }{-8p} $ Distribute the negative sign: $z = \dfrac{4p + 5 - 24p}{-8p}$ $z = \dfrac{-20p + 5}{-8p}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{20p - 5}{8p}$